Open Access
Translator Disclaimer
2013 Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data
Young-Doo Kwon, Soon-Bum Kwon, Bo-Kyung Shim, Hyun-Wook Kwon
J. Appl. Math. 2013: 1-8 (2013). DOI: 10.1155/2013/471731

Abstract

This study examined the characteristics of a variable three-point Gauss quadrature using a variable set of weighting factors and corresponding optimal sampling points. The major findings were as follows. The one-point, two-point, and three-point Gauss quadratures that adopt the Legendre sampling points and the well-known Simpson’s 1/3 rule were found to be special cases of the variable three-point Gauss quadrature. In addition, the three-point Gauss quadrature may have out-of-domain sampling points beyond the domain end points. By applying the quadratically extrapolated integrals and nonlinearity index, the accuracy of the integration could be increased significantly for evenly acquired data, which is popular with modern sophisticated digital data acquisition systems, without using higher-order extrapolation polynomials.

Citation

Download Citation

Young-Doo Kwon. Soon-Bum Kwon. Bo-Kyung Shim. Hyun-Wook Kwon. "Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data." J. Appl. Math. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/471731

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950692
MathSciNet: MR3147903
Digital Object Identifier: 10.1155/2013/471731

Rights: Copyright © 2013 Hindawi

JOURNAL ARTICLE
8 PAGES


SHARE
Vol.2013 • 2013
Back to Top